Hydrodynamic exploration in variable density environments



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HYDRODYNAMIC EXPLORATION IN VARIABLE DENSITY ENVIRONMENTS Filed April 50, 1964 4 Sheets-Sheet 1 loco STRUCTURE 0 MILES 25 W S y W v 4,? WW d f Y Z? M ZW w Y 0 E N s ITY QQMJLE E3. 2

E GRbUND 'WATER m Feb. 14, 1967 c. w. BROWN ETAL.

HYDRODYNAMIG EXPLORATION IN VARIABLE DENSITY ENVIRONMENTS Filed April 50, 1964 4 Sheets-Sheet 2 FLOWING PRESSURE (/7) MAP (psi) 0 MILES Feb. 14, 1967 c, w. BROWN ET AL 3,303,704

HYDRODYNAMIC EXPLORATION IN VARIABLE DENSITY ENVIRONMENTS Filed April 30, 1964 4 Sheets-Sheet 5 FRESH WATER h MAP i1 LOCAL DENSITY MEAN DENSITY f Feb. 14, 1967 c. w. BROWN ET AL 3,303,704

HYDRODYNAMIC EXPLORATION IN VARIABLE DENSITY ENVIRONMENTS Filed April 50, 1964 4 Sheets-Sheet 4 3 O c 0 IOOO K \/\\X I .93 7r VALUES hw FOR LOCAL 200 FLUID DENSITY 00 I 20o0' 2 9 q I -4000 [U l 6000 L 2000 V-PARTS MILLION HYDROSTATIC =.43 +2500 pwg p g=.47 20o +2000 0 4: O a O 0 200 g3 I529 7TVALUES N g zooo h FOR LOCAL FLUID DENSITY w -4000 LLI 600 0 -PART$ MILLION HYDRODYNAMIC .9 10 INVENTORS CZm /as W $70M BY c z'amey fZuZ/w United States Patent 3,303,704 HYDRODYNAMIC EXPLORATION IN VARIABLE DENSITY ENVIRGNMENTS Charles W. Brown, Arlington, and Sidney M. Foulks,

Irving, Tex., assignors to Mobil Oil Corporation, a

corporation of New York Filed Apr. 30, 1964, Ser. No. 363,784 9 Claims. (Cl. 73-432) This invention relates to exploration for entrapped accumulations of fluid hydrocarbons, and more particularly to the determination of forces in an aquifer of varying fluid density.

Exploration hydrodynamics deal with oil migration and accumulation in a physical and chemically dynamic ground water environment. Before coming to rest in a reservoir, oil migrates and gathers as a minority fluid in a ground water system. The importance of the relationship between oil and moving ground water has been recognized. Pressure-induced flow in porous media may be understood from the well known work of Darcy and Muskat. Further, in a paper entitled, Entrapment of Petroleum Under Hydrodynamic Conditions, by Hubbert, American Association of Petroleum Geologists Bulletin, volume 37, page 1954-2026, measurement of ground Water parameters as an exploration tool is disclosed.

It has been found that such hydrodynamic theory is valid only for systems in which ground Water density is constant. Density is a function of chemical composition, temperature, and pressure. In accordance with the present invention, actual flow-inducing pressure gradients are determined, recognizing that these gradients are the forces that cause ground water to migrate through rock formations. In order to arrive at actual flow-inducing pressure gradients, it is necessary to make a detailed evaluation of the salinity and density of the aquifer.

More particularly, in accordance with the invention, formation pressures are measured at a plurality of spaced points in an aquifer. The elevations are also measured for each point at which such pressures are measured. The differences in static pressure between the points based upon local density variations within the aquifer between said elevations are computed. For each pair of pressure measurement points, the difference between the measured pressure differential and the computed static pressure differential is plotted in correlation With the locations of the measurement points.

For a more complete understanding of the present invention and for further objects and advantages thereof, reference may now be had to the following description taken in conjunction with the accompanying drawings in which:

FIGURE 1 illustrates an inclined aquifer with variable fluid density hydrostatic conditions;

FIGURE 2 is a structural contour map of a representative basin;

FIGURE 3 is a plot of ground water density in the basin of FIGURE 2;

FIGURE 4 is a plot of flowing pressure (1r) for the basin of FIGURE 2, based upon operations of the present invention;

FIGURE 5 is a diagram illustrating computations involved in determining the values plotted in FIGURE 4;

FIGURE 6 is a potentiometric map (11 in accordance with prior art methods for comparison with FIG- URE 4 where the density of fresh water is employed;

FIGURE 7 is a map similar to FIGURE 6 in which the potentials are based upon mean density;

FIGURE 8 is a map similar to that of FIGURE 6 Where the potentials are based upon local density;

3,303,704 Patented Feb. 14, 1967 'ice FIGURE 9 illustrates the results of the present invention compared with prior art techniques for a static condition; and

FIGURE 10 illustrates the results of the present invention compared with prior art techniques for a dynamic condition.

In contrast with prior procedures, the present invention provides for determination of actual flow-inducing pressure gradients, or the flowing pressure forces in an aquifer. Only when such forces are known can the determinations of oil potentials be carried out with reliability essentially in the manner disclosed by Hubbert. The mapping of flow-inducing pressure gradients is undertaken to provide a simpler and more accurate way of describing dynamic ground water systems.

In using the hydrodynamic exploration tool, the chief problem is to determine whether a ground water system is static or dynamic. If it is dynamic, then the rate and direction of fluid motion must be determined to provide a means for analyzing the effect of this motion on petroleum accumulations.

In order to understand the forces involved, reference will hereinafter be made to a concept of a generalized potential. Such water potentials is the quantity which indicates the direction water will move if motion thereof is possible. Potential is defined in the present case in the usual sense, in that motion will be from a point of high potential to a point of low potential. A water poten tial is such that the negative of its gradient is the force acting on the Water.

In a constant density system, the water heads at spaced wells will have the same heights h under static conditions. That is, if manometers are located in a static aquifer at each of a plurality of lateral spaced points,

and if the density is constant, the Water will rise in the manometers to the same height h at each of the points. Thus, when a plane is passed through the points h the potentiometric surface will be horizontal. However, if the system is dynamic, the surface will be inclined in the direction of flow.

In a horizontal aquifer in which fluid density is uniform, fluids will migrate through the formation in response to formation pressure gradients. If the-re are accurate pressure measurements in a horizontal aquifer, it is relatively easy to determine whether the fluid system is static or dynamic. If two pressures P and P measured at laterally spaced points in an aquifer, are equal, there is no force tending to cause flow between the points of pressure measurement. However, if P #P there is a force tending to cause flow from the higher pressure to the lower pressure.

In an inclined aquifer, it is not easy to determine whether the pressure difference between two measuring points indicate a static or a dynamic system. For example, assume that P and P are the pressures measured at two laterally spaced points in an inclined aquifer at elevations Z and Z If the system is static, the pressure P will equal P minus the static pressure difference between the two Wells. Between any two pressure control points, the static pressure difference equals the static pressure gradient times the difference in elevation. In contrast, actual measured formation pressure differences may be greater than, equal to, or less than the calculated static pressure difference.

For the purpose of the present description, the flowing pressure difference will be identified as A1,. This is the actual pressure difference causing fluid flow through the aquifer. The function A1r represents the departure from hydrostatic conditions.

The problem is illustrated in FIGURE 1 showing a two-dimensional plot of a segment of an aquifer 10.

Aquifer 10 may be bounded at the interface 11 by an impervious strata. Aquifer 10 may be sand through which water may flow or in which ground water is found. A plurality of wells, including wells 21 and 22, penetrate aquifer 10. In accordance with the invention, the formation pressures P and P are measured in wells 21 and 22 by use of units 13 and 14 which may include pressure sensors such as well known in the art. Pressure signals are transmitted to the earths surface by way of channels 15 and 31. The signals are representative of the formation pressure in wells 21 and 22. In addition, the elevations of points of pressure measurement in wells 21 and 22 are measured by usual means such as unit 18 coupled to the winch cable forming channel 15. Ground water densities are measured in wells 21 and 22 and in the wells in which points A, B, C and D are located. Such measurements may be made by suitable density measuring means in units 13 and 14. Thus, for wells 21 and 22, formation pressure, fluid density, and the depths at which the measurements are made, are represented at the earths surface by electrical signals.

Ordinarily, the measurement of formation pressure is time-consuming and expensive. Thus, only a minimum number of points are assigned for pressure measurement in a given field. However, determinations of formation water density are less involved and are generally more numerous.

For each section of the aquifer, there may then be determined a formation water density function in terms of p the density, and g, the force of gravity. The function p g is the vertical hydrostatic pressure gradient.

In FIGURE 1, g) is the vertical hydrostatic pressure gradient in the section between well 21 and point A. In a similar manner, the gradients (p g) g) are determined. The gradients are then employed to determine the static pressure difference AP between wells 21 and 22. 'i

More particularly, to determine the static pressure differences between wells 21 and 22, the static pressure changes across the areas of known mean density between wells 21 and 22 are algebraically added. That is, the static pressure difference between well 21 and point A is added to the differences between points A and B, points B and C, points C and D, and point D and well 22.

If the system is static, it will be found that the sum of the static pressure differences equals the measured pressure differences between the wells 21 and 22. If the two are not equal, then the difference between measured pressure differential and the static pressure differential is the flowing pressure differential A1r.

When A1r values are mapped, the gradient 1r is the flowing pressure force parallel to the bedding planes. It will be noted that the negative of the gradient 71' will indicate the rate and direction of flow in constant density ground water systems, as well as where the density is variable.

In accordance with the invention, data such as mapped in FIGURE 2 shows the structure of the aquifer. Data for the same area showing the formation water density preferably is obtained and conveniently portrayed in contour form as illustrated in FIGURE 3. The results to be achieved by the present invention are illustrated for one case in FIGURE 4, wherein the flowing pressure 1r in the aquifer is contoured.

With the data shown in FIGURES 2 and 3 available, and with pressure measurements available for selected spaced points throughout the area contoured in FIGURES 2 and 3, the flowing pressure 1r may be mapped to portray graphically the fiow pattern in the area of interest. The present invention relates to the determination of the variations from point to point in the flowing pressure and the portrayal thereof on an areal basis.

In FIGURE 1, the wells 21 and 22 penetrate an aquifer 10. Points A, B, C and D in additional wells are at spaced points in the aquifer 10. Pressures, densities, and depths are then measured for developing a flowing pressure func- 4 tion descriptive of flow between the locations of wells 21 and 22.

Pressure dependent signals on lines 15 and 31 are applied to a surface system which includes adding networks 32 and 33. One input to the adding network 32 is the inverse of the measured formation pressure at well 21, i.e. -P as it appears at the output of inverter 51.

A signal representative of the values of the hydrostatic pressure gradient g) and a signal representative of the depth interval AZ are applied to the two input terminals of a multiplier 41. The depth of unit 13 as sensed by unit 17 is subtracted in unit 19 from the depth of point A as sensed by unit 18 to produce the signal AZ. The output of multiplier 41 is applied to adding network 32. In a similar manner, multipliers 42, 43, 44 and 45 produce at their output terminals incremental static pressure difference signals which are applied to adding network 32.

A pressure signal from unit 14 in well 22 is applied to adding network 33 so that at the output terminal, the output signal is representative of the flowing pressure difference between wells 21 and 22 (A1r If, in FIGURE 1, the density of the fluid varies with increasing depth, the computation of the value P may be as follows:

Where the system of FIGURE 1 is dynamic, knowing the measured pressures P =2000 p.s.i. and P =250O p.s.i., it would be found that AP#AP Applying the equation A1r=APAP the magnitude and direction of the flowing presurre differental A1r may be determined. For the above example, A1r=25002000578=-78 p.s.i.

It is convenient to write the expression AP using a summation sign in the form In order better to understand the improvement achieved by the present invention, reference may now be had to FIGURES 6-8. A comparison of FIGURE 4 with FIG- URES 68 will provide an understanding of the error which may be incurred using prior art methods. In FIG- URES 68, a potentiometric function h based upon certain average or local densities, has been employed to define flow. Data representative of forty-two pressure control wells is included. At each well, the formation pressure was determined in order to outline the possible flow pattern.

The data in FIGURE 6 illustrates a potentiometric plot h using the density of fresh water for the reference fluid. In FIGURE 6, there is an area of high potential at the north edge of the map with suggested fl-ow to the south, east and west. Immediately south of this feature is a broad sink into which water appears to flow from all directions. The contour interval of the potentiometric map of FIGURE 6 is roughly feet of water head which is roughly equivalent to 50 psi. of flowing pressure 1r on the map of FIGURE 4. A large high potential area is present along the axis of the basin. Water would flow outward from this high in all directions.

FIGURE 7 is a map of the same basin wherein the data is computed on the basis of average basin ground water density.

FIGURE 8 shows the same map when the potential h.,, is based upon local ground water densities. The direction of flow is not grossly distorted except in areas shown as sinks. However, the flow rate along the west basin is exaggerated by a factor of as much as five relative to the flow pattern shown in FIGURE 4.

From a comparison of the map of FIGURE 4 and any one of the maps of FIGURES 6-8, it will readily be apparent that the use of the potentiometric value h, leads to error. The nature of the error is graphically demonstrated in FIGURES 9 and 10 where a hydrostatic condition and a hydrodynamic condition, respectively, are illustrated. In both cases, variations in ground water density are present.

In FIGURES 9 and 10, the aquifer is illustrated as having a constant slope with measured pressures, salinity, and respective values for the function (p g) being plotted. By following the teaching of the present invention, the curve of r VALUES is obtained. The data defines a horizontal line. This is the expected result where the system is static. However, using the prior art methods, based upon fresh water g=0.43), average density g= 0.47), or local fluid density for determining h functions are obtained which would indicate that the system is not static. The three curves indicate a moving system. Two of them indicate flow in one direction therebetween. The third indicates flow in the opposite direction. The most nearly correct results are shown in the plot of the function 1r, where the straight horizontal line shows flow to be zero.

In FIGURE 10, flow is in the direction of the arrow in the aquifer. Again, the difference between the flow patterns depicted by the various method of analysis is illustrated by curves corresponding with those of FIGURE 9. The wide variation in the flow rates depicted by the four sets of data is graphically portrayed. The r VALUES represent the most nearly correct values of flow.

The conditions depicted in FIGURES 9 and 10 emphasize the necessity for avoiding the use of the potentiometric function h and the desirability of determining the 1r VALUES in order properly to understand the flow pattern in a given formation.

When the flowing pressure forces or 11' VALUES in an aquifer are known, as shown in FIGURE 4, then it is an easy matter to derive oil potentials in terms of this new quantity by then following the teachings of Hubbert. In all cases, however, the usefulness of the oil potential determination is dependent upon the accurate determination of the rate and direction of ground water movement. There is provided herein an understanding of and a means for determining accurately the ground water movement, where prior system are characterized by the inherent introduction of error.

The density measuring means in units 13 and 14, for use at points A-D, may be of the type described in US. Patent No. 3,123,709 to Caldwell et al. In accordance with this method of measuring fluid density in a borehole, the transmission through a column of fluid of radiation from a radioactive source is measured and a signal is produced which i calibrated in terms of fluid density. In FIGURE 1, a fluid density function measured at point A is applied to one input terminal of multiplier 41.

It is to be understood that, as shown in FIGURE '5, the function g) of FIGURE 1 may be employed in multiplier 41 by measuring densities at the location of unit 13 and at point A and generating an average signal therefrom. The signal (p g) applied to one terminal of multiplier 41 is dependent to the average of the two measured densities. Rather than measure the density as above noted, water sample frequently are collected and are analyzed chemically to provide density data.

The measurement of formation fluid pressure may be accomplished by use of well known borehole pressure measuring instruments. More particularly, it is necessary to determine the initial or original formation fluid pressure. This is ordinarily determined through a conventional drill stem test in connection with the drilling operation. Alternatively, the pressure measurement may be made through use of any one of many logging services currently offered by service companies. Representative of such services is the wire line formation testing service offered on a commercial basis by Schlumberger Limited of Houston, Texas.

The system at FIGURE 1 includes in block form a number of components which, in general, are well known in the art and for this reason are not shown in detail. For example, the subtraction unit 19 may be of the type described in Waveforms, Radiation Laboratory Series, volume 93, McGraw-Hill (1947) in the section entitled Addition and Subtraction of Voltages and Currents, page 629. A suitable subtraction unit is described at page 642 under the heading Cathode Coupling. Summing units to carry out the functions of adders 32 and 33 are also disclosed in the same section. A suitable network is shown in Figure 18.1 at page 631 of the above reference. Multiplying networks 41-45 may be of the type disclosed in US. Patent 2,982,942 to J. E. White.

While the system has been illustrated in a simplified form in FIGURE 1 for producing a 1r VALUE indicative of flow between wells 21 and 22, it will be appreciated that data representative of formation pressure, depths, and densities may be employed in general computer system to produce a map as in FIGURE 4. Input data may be programmed such that a computer will automatically plot the flowing pressure map illustrated in FIGURE 4. Such computational and plotting procedures of the complexity involved in the present case are well known in the art. More particularly, Bulletins No. 122 and 151B published by California Computer Products Incorporated, 305 Muller Avenue, Anaheim, California, disclose techniques for utilization of plotters in conjunction with computer systems. Bulletin 151B describes a Plotter Subroutine Package for using a Calcomp plotter with a computer manufactured and sold by Control Data Corporation of Minneapolis, Minnesota, and identified as Model CDC1604. Suitable plotters are manufactured and sold by California Computer Products Incorporated and are identified as Models 564 and 566. That such mapping procedures are generally well known is shown by an article in the Oil and Gas Journal, August 5, 1963, at page 158. Results of use of such procedures is illustrated in the publication of the American Geological Institute, Geotimes, April 1964, volume VIII, No. 7, page 70.

Thus, in accordance with the invention, there is provided a method for use in the location of deposits of liquid hydrocarbons in an aquifer. Physical functions are generated representative of formation fluid pressure at each of a plurality of laterally spaced points in the aquifer. The functions are modified in dependence upon the relative elevations of the points and the variations with depth in the density of the fluid in the aquifer between the points of pressure measurement. From selected points of the modified functions, a hydrodynamic flow-inducing pressure function is generated and registered in correlation with locations of the selected pairs of points.

Having described the invention in connection with certain specific embodiments thereof, it is to be understood that further modifications may now suggest themselves to those skilled in the art and it is intended to cover such modifications as fall within the scope of the appended claims.

What is claimed is:

1. The method of exploration for location of deposits of liquid hydrocarbons in an aquifer which comprises:

(a) generating physical functions representative of the formation fluid pressure at each of a plurality of laterally spaced points in said aquifer,

(b) modifying said functions in dependence upon the relative elevations of said points and the variations in density of the fluid between said points,

(c) generating from selected pairs of the modified functions hydrodynamic flow-inducing pressure gradient functions, and

(d) registering said functions in correlation with the locations of the points from which said modified functions are derived.

2. In hydrodynamic exploration for entrapment of oil, the method of determining flowing pressure differences between two points which comprises:

(a) measuring formation pressures P and P at two laterally spaced points,

(b) measuring the depths Z and Z of the points at which the pressures are measured,

(c) measuring the ground Water density at said two points and at a plurality of locations therebetween, and

(d) generating an electrical function representative of the flowing pressure differential Aw between said two points in accordance with the expression where:

p is the density of the ground water between said points and said locations;

g is the force of gravity; and

n is the number of distance increments between said points.

3. In the method of hydrodynamic exploration for entrapment of fluid hydrocarbons, the steps of:

(a) measuring the formation pressures at a plurality of laterally spaced points in an aquifer,

(b) measuring the elevations of said points,

(c) generating a signal representative of the static pressure differential between the measured elevations on the basis of local densities within the aquifer between said elevations, and

(d) for each pair of pressure measurement locations,

generating an automatically sensible physical function representative of the difference between the measured pressure differential and said static pressure differential.

4. In the method of hydrodynamic exploration for entrapment of fluid hydrocarbons, the steps of:

(a) generating a first function representative of the pressure differential between two laterally spaced points in an aquifer,

(b) generating a second function representative of the static pressure differential between said points on the basis of local densities within the aquifer between said points, and

(c) generating a third function representative of the difference between the measured pressure differential and said static pressure differential.

5. In the method of claim 4, the improvement which comprises repeating steps a-c for each of a plurality of pairs of points having areal distribution in said aquifer, and registering each said third function in correlation with the coordinates of the vertical projections of the locations of said points.

6. A system for determining the flow-producing pressure differential between two points in an aquifer which comprises:

(a) means for producing a pair of functions representative of the formation fluid pressures at said points,

(b) means for producing a plurality of functions representative of the depths of the points of pressure measurement and of locations n n m,

(c) means for producing a plurality of functions representative of the vertical hydrostatic pressure gradients in the fluid at the points of pressure measuren between where:

AP:P2P1

p represents the densities of the ground water between said points and said locations, and g is the force of gravity,

7. A system for determining the flow-producing pressure differential between two points in an aquifer which comprises:

(a) borehole exploring units each having means for producing a pair of functions representative of the formation fluid pressures at said points,

(b) means at least in part included in said units for producing a plurality of functions representative of the depths of the points of pressure measurement and of locations n n n (0) means for producing a plurality of functions representative of the vertical hydrostatic pressure gradients in the fluid at the points of pressure measurement and at said locations n n n between said points of pressure measurements, and

(d) means for generating an electrical signal representative of the flowing pressure differential A1r between said two points in accordance with the expression Ar AP- APS where:

AP=P P 11 AP,: g) (AZ) and p represents the densities of the ground water between said points and said locations, and g is the force of gravity.

8. The method of exploration for location of deposits of liquid hydrocarbons in an aquifer which comprises:

(a) converting fluid pressure at each of a plurality of laterally spaced points in said aquifer into automatically reproducible physical functions represen tative of such formation pressures,

(b) converting indications of the relative elevations of said points into first modifying functions,

(0) converting variations in density of the fluids between said points into second modifying functions,

(d) automatically modifying said physical functions in dependence upon said modifying functions,

(e) generating from pairs of the modified functions hydrodynamic flow-inducing pressure gradient signals, and

(f) recording said flow-inducing pressure gradient signals in correlation with the locations of the points from which said modified signals are derived.

9. The method of exploration for location of deposits of liquid hydrocarbons in an aquifer which comprises:

(a) converting fluid pressures at each of a plurality of laterally spaced points in said aquifer into automatically sensible signals which in magnitudes are representative of the respective magnitudes of said pressures,

(b) converting relative elevations of said points into (e) automatically modifying said automatically sensible signals in dependence upon said first modifying signals and said second modifying signals,

(f) automatically generating from selected pairs of the modified signals hydrodynamic flow-inducing pressure gradient signals, and

(g) registering said pressure gradient signals in spatial relationships which are representative of spatial re- Hubbert, Entrapment of Petroleum Under Hydrodynamic Conditions, Amer. Assoc. Petrol. Geologists Bulletin, vol. 37, August 1953, pages 1986-1992.

DAVID SCHONBERG, Primary Examiner. 

1. THE METHOD OF EXPLORATION FOR LOCATION OF DEPOSITS OF LIQUID HYDROCARBONS IN AN AQUIFER WHICH COMPRISES: (A) GENERATING PHYSICAL FUNCTIONS REPRESENTATIVE OF THE FORMATION FLUID PRESSURE AT EACH OF A PLURALITY OF LATERALLY SPACED POINTS IN SAID AQUIFER, (B) MODIFYING SAID FUNCTIONS IN DEPENDENCE UPON THE RELATIVE ELEVATIONS OF SAID POINTS AND THE VARIATIONS IN DENSITY OF THE FLUID BETWEEN SAID POINTS, (C) GENERATING FROM SELECTED PAIRS OF THE MODIFIED FUNCTIONS HYDRODYNAMIC FLOW-INDUCING PRESSURE GRADIENT FUNCTIONS, AND (D) REGISTERING SAID FUNCTIONS IN CORRELATION WITH THE LOCATIONS OF THE POINTS FROM WHICH SAID MODIFIED FUNCTIONS ARE DERIVED. 